Calculus

# Characteristics of f, f', f''

Let $f$ be a function such that $f(0)=50.$ If the above graph represents the graph of the first derivative of $f$ on the interval $0 which of the following is the correct description of $f$ on this interval?

For the function $y=x^3+x^2-x-1,$ determine the interval where $y$ is decreasing.

Suppose $f$ is a function such that $f(0)=33$ and the first derivative of $f$ on the interval $-2 < x < 2$ is as shown in the above diagram. Which of the following is the correct description of the function $f$ on this interval?

Suppose $f$ is a function defined on the closed interval $-3 \le x \le 4$ with $f(0)=42,$ such that the graph of $f',$ the derivative of $f,$ on the interval is as shown in the above diagram. On what intervals is $f$ increasing?

Suppose $f$ is a function defined on the closed interval $-3 \le x \le 4$ with $f(0)=3$ such that the graph of $f',$ the derivative of $f,$ on the interval is as shown in the above diagram. Find the $x$-coordinates of the points of inflection of $f.$

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